1. Technical Field
The present invention relates to signal enhancement, and more particularly, to a system and method for nonlinear signal enhancement that does not use a noisy phase of a signal.
2. Discussion of the Related Art
Current signal enhancement techniques are directed to suppressing noise and improving the perceptual quality of a signal of interest. For example, by using signal enhancement algorithms, signal enhancement techniques can remove unwanted noise and interference found in speech and other audio signals while minimizing degradation to the signal of interest. Similarly, image enhancement techniques aim to improve the quality of a picture for viewing. In both cases, however, there is room for improvement due to the random nature of noise and the inherent complexities involved in speech and signal recognition.
Current signal enhancement techniques follow the approach shown, for example, in FIG. 1. As shown in FIG. 1, a linear transformation such as a Fourier transform is applied to a noisy signal giving a representation of the signal in the transformed domain (110). The modulus or absolute value of the transformed signal is then determined (120) and a statistical estimate of a noise free part of the signal is computed (130). As the statistical estimate is being computed, the phase of the transformed signal is found (140). The product of the statistical estimate and the phase of the transformed signal is then determined (150) and an inverse linear transform is applied to the product to invert the product back into its original domain (160), thus resulting in a cleaned version of the signal.
Such algorithms have been shown to yield significant improvements for large classes of signals. However, recent psychoacoustic studies have shown that signal quality is very dependent on phase estimation. For example, if one takes a speech signal, performs a Linear Predictive Coding analysis and uses random white noise for excitation, the reconstructed signal in the time domain sounds very machine-made. Yet, if one uses custom excitation signals, the signal quality improves dramatically; however, this technique requires an estimate of the signal phase.
In order to enhance signal quality, information loss that results when taking the modulus of a signal has been considered. For example, in optics-based applications, a discrete signal may be reconstructed from the modulus of its Fourier transform under constraints in both the original and Fourier domain. For finite signals, the approach uses the Fourier transform with redundancy, and all signals having the same modulus of the Fourier transform satisfy a polynomial factorization. Thus, in one dimension, this factorization has an exponential number of possible solutions and in higher dimensions, the factorization is shown to have a unique solution.
Accordingly, there is a need for a technique of accurately reconstructing a signal without using its noisy phase or estimation and that takes into account information loss of the modulus of the signal.